Yes you can work in a hospital.
If you choose a career in healthcare management, your first job might be an entry- to mid-level management position in a specialized area, such as:
Marketing and public affairs
Material management (purchasing of equipment and supplies)
Medical staff relations
Patient care services
Planning and development
In the above fields, Some examples of non-clinical hospital jobs:
Case manager / Social Worker
Human Resources & Recruiting
Executives - CEO, CFO, CIO.